Make the batter. Heat the oven to 350 degrees. In a blender or food processor, combine the corn, eggs and sweetened condensed milk. Process to a coarse puree—leave a little of the corn’s texture, but no whole kernels. In a small bowl, whisk together the flour, baking powder, salt and cinnamon. In a stand mixer (fitted with the paddle attachment if available), beat the butter until light and fluffy. Beat in the corn mixture in 3 additions, alternating with the flour mixture.
Bake. Oil the bottom and sides of a 9-inch round cake pan or an 8x8-inch square cake/brownie pan. Line with parchment paper, oil the parchment, then dust everything with flour, inverting and tapping the pan over your sink or garbage can to remove any excess. Scrape the batter into the pan, smooth the top and bake in the center of the oven for 50 to 60 minutes, until browned and no longer jiggly in the center. (A toothpick inserted in the center will come out almost clean.) Cool for 10 minutes, then turn out onto a cooling rack. Immediately invert onto a serving plate (the top of this cake is its prettiest part).